90=48t-6t^2

Solution for 90=48t-6t^2 equation:

Simplifying
90 = 48t + -6t2

Solving
90 = 48t + -6t2

Solving for variable 't'.

Reorder the terms:
90 + -48t + 6t2 = 48t + -48t + -6t2 + 6t2

Combine like terms: 48t + -48t = 0
90 + -48t + 6t2 = 0 + -6t2 + 6t2
90 + -48t + 6t2 = -6t2 + 6t2

Combine like terms: -6t2 + 6t2 = 0
90 + -48t + 6t2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + -8t + t2) = 0

Factor a trinomial.
6((3 + -1t)(5 + -1t)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {3, 5}